# Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space

@article{Lawrie2015GapEA, title={Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space}, author={Andrew Lawrie and Sung-Jin Oh and Sohrab Shahshahani}, journal={arXiv: Analysis of PDEs}, year={2015} }

## 16 Citations

Equivariant Wave Maps on the Hyperbolic Plane with Large Energy

- Mathematics
- 2015

In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is the hyperbolic plane…

Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case.

- Mathematics
- 2017

In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation in the subcritical perturbation class. This result may…

Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution

- MathematicsCommunications on Pure and Applied Mathematics
- 2021

We consider the Cauchy problem for the Schr\"odinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the…

The Cauchy problem for wave maps on hyperbolic space in dimensions $d \geq 4$

- Mathematics
- 2015

We establish global well-posedness and scattering for wave maps from $d$-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical…

On Global Dynamics of Schrödinger Map Flows on Hyperbolic Planes Near Harmonic Maps

- MathematicsCommunications in Mathematical Physics
- 2022

The results of this paper are twofold: In the first part, we prove that for Schrodinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic…

Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces

- MathematicsDiscrete & Continuous Dynamical Systems - A
- 2019

In this paper, we prove that the solution of the Landau-Lifshitz flow $u(t,x)$ from $\mathbb{H}^2$ to $\mathbb{H}^2$ converges to some harmonic map as $t\to\infty$. The essential observation is that…

Equivariant Schr\"odinger maps from two dimensional hyperbolic space

- Mathematics
- 2017

In this article, we consider the equivariant Schr\"odinger map from $\Bbb H^2$ to $\Bbb S^2$ which converges to the north pole of $\Bbb S^2$ at the origin and spatial infinity of the hyperbolic…

Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms

- Mathematics
- 2017

In this note, we will review our recent work on the asymptotic behaviors of nonlinear Klein-Gordon equation with damping terms and LandauLifschitz flows from Eucliedean spaces and hyperbolic spaces.…

Asymptotic stability of small energy harmonic maps under the wave map on 2D hyperbolic space

- Mathematics
- 2017

In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map. This result may be seen as an example supporting the soliton…

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